#### Vol. 11, No. 8, 2017

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Torsion orders of complete intersections

### Andre Chatzistamatiou and Marc Levine

Vol. 11 (2017), No. 8, 1779–1835
##### Abstract

By a classical method due to Roitman, a complete intersection $X$ of sufficiently small degree admits a rational decomposition of the diagonal. This means that some multiple of the diagonal by a positive integer $N$, when viewed as a cycle in the Chow group, has support in $X×D\cup F×X$, for some divisor $D$ and a finite set of closed points $F$. The minimal such $N$ is called the torsion order. We study lower bounds for the torsion order following the specialization method of Voisin, Colliot-Thélène, and Pirutka. We give a lower bound for the generic complete intersection with and without point. Moreover, we use methods of Kollár and Totaro to exhibit lower bounds for the very general complete intersection.

##### Keywords
algebraic cycles, decomposition of the diagonal
Primary: 14C25